A question about torsion

If you're working in the 3-limit, and you tempered out the square of
the pythagorean comma, you end up with a periodicity block that's 24
notes long. Upon eliminating the comma, 12 of those notes match up
with 12 of the other notes, so you end up getting 12 pitches.

This is torsion, right? How could this be detected beforehand, since
there's only one comma being tempered out and hence nothing with which
to get the GCD of.

-Mike

Mike wrote:

>If you're working in the 3-limit, and you tempered out the square of
>the pythagorean comma, you end up with a periodicity block that's 24
>notes long. Upon eliminating the comma, 12 of those notes match up
>with 12 of the other notes, so you end up getting 12 pitches.
>
>This is torsion, right?

Yep.

>How could this be detected beforehand, since
>there's only one comma being tempered out and hence nothing with which
>to get the GCD of.

I remove it afterhand (GCD of the val elements).

-Carl

On Tue, Sep 7, 2010 at 6:09 PM, Carl Lumma <carl@lumma.org> wrote:
>
> >How could this be detected beforehand, since
> >there's only one comma being tempered out and hence nothing with which
> >to get the GCD of.
>
> I remove it afterhand (GCD of the val elements).
>
> -Carl

But there's only one comma, so only one val, right? So wouldn't the
GCD of any val and itself be itself?

-Mike

>But there's only one comma, so only one val, right?

Right.

>So wouldn't the GCD of any val and itself be itself?

The val elements will be reducible (try it!).

-Carl

On 8 September 2010 05:32, Mike Battaglia <battaglia01@gmail.com> wrote:

> This is torsion, right? How could this be detected beforehand, since
> there's only one comma being tempered out and hence nothing with which
> to get the GCD of.

The Pythagorean comma in vector form is [-19, 12>. It's square is
[-38, 24>. That's what you're tempering out and you can find the GCD
of it.

Graham

Oh, duh. I get it now. Thanks

-Mike